Coulomb bound state
= Coulomb bound state
{c}
{title2=$E_N=-m\gamma^2/(2\hbar^2N^2)$}
A Coulomb bound state is a physical normalizable eigenfunction for an attractive potential $V(r)=-\gamma/r$, $\gamma>0$. For the usual regular boundary condition at the origin its energies are the displayed values, $N=1,2,\ldots$. The spherically symmetric states have <orbital angular momentum> zero; <series-termination quantization of the Coulomb radial equation> constructs them as a polynomial times a decaying exponential. Square integrability on the punctured radial interval alone does not replace the physical condition at the origin.